Wave filter



Nov'. 3, 1925. 1,559,638'

W. H. MARTN "WAVE FILTER Filed April 26, 1920 (Wwf/arl] x 6, 52x52 lATTORNEY IN1/'EN TOR.

'Patented Nov. 3, 1925.

WILLIAM H. MARTIN, or NEW YORK, N. Y.,

TCELEGRAPH OMPANYQACORPORATION 0F N EW YORK.

Application led April 26, 1 920. Serial No. 376,763.

To all who-m t may concern:

Be it known that I, IVILLIAII residing Bronx and State of New York, haveinvented certain Improvements in fave Filters, of which the following isa specification.'

-My invention relates to wave filters for use in electric circuits where'it is desired to transmit frequencies and to suppress, or partlysuppress, currents of other frequencies.A More particularly, generaltypeillustrated and described vin the atents to George A.. Campbell,1,227,- 113 and 1,227,1145iss'ued May22, 1917.

The presentl invention proposes a filter which freely transmits allfrequencies in a range between certain pre-assigned limits, neither of'which is zero or infinity, and which attenuates frequencies outside thisrange; The filter of the. presentinvention is characterized by havingtheoretically infinite attenuationyat a finite frequency other than zeroand lying in the attenuated range.' It may consequently be so designedthat it vwill effect substantially complete suppression of anyv desired.frequency outside the H. MARTIN.

transmitted band, or it may be so propor-4 tioned, that the frequency ofinfinite attenuation is close to either limit ofthe transmitted band, sothat a very sharp cut-off action may be attained at the said limit. vAsin the Campbell filters, all frequencies. within the attenuatedrange-can be suppressed to any desired degree by use of a sufficientlylarge number of sections. The -special feature of this filter, however,lies in the fact that the attenuation per section is substan-4 tiallyinfinite for one frequency which can be freely chosen within thespecified limits. A good understanding of the invention may now be hadfrom the following description of one form of embodiment thereof,reference being had to the accompanying drawing in which,

Fig. 1 is a diagrammatic View showing one form of embodiment of theinvention;

Figsf 2 and 3, diagrams showing graphically the attenuationcharacteristics of the filter ofFig. 1; and l Fig. 4, a diagrammaticview showing one form of termination of the filter. I

at New York, in the county of alternating current of selected itconcerns 'wave filters of the C, and that of Fig.

AssIGNon To AMERICAN TELEPHONE AND.

Similar characters of reference designate similar partsin each'of theseveral views. In the form shown in Fig.` 1l the filter comprises anumber of sections or elements each of which consists of a lumpedimpedance Z1 1n 'series wlth the line 1 and a lumped impedance Z', in.shunt to the line. i

The impedances Z1 and ZZ* are shown as comprlsed of inductances L, andll.,2 in series withcapacities C, and (G2, .'respectively.

lBothserie's and shuntl impedancesfare thus constituted of like types-of resonant circuits, a feature. which distinguishes them from thefilt'ersidisclosed in the Campbell patents hereinbefore referred to,'incertain of which filters theseries imnedances con'- sist of one type'ofresonant. circuits (i. e.. series) and the shunt impedances, 'of an#other type of resonant circuits, (i. e., parallel or anti-resonant). f if I have found that the. type of filter of this invention has certainadvantageous charaeteristics which I shall presently explain withreference to Figs. 2 and .3, whichshow graphically the' attenuationcharacteristics of filters similar to that of Fig;l 1, the abseissaerepresenting frequencies and the ordinates, values of attenuation. The'curve of Fig. 2' shows the attenuation for the genera-l case in whichthe numerical product of L1.

timesI C1 is'greater than that ofL2 times the reverse is true. It willbe observed that the attenuation is nil only for the band of frequencieslying between fo and f3, this be-v ing the transmitted band. 'Theattenuation y is a maximum at the'frequency f2, being theoreticallyequal to infinity. When f2 is close to f3, theslope of the attenuationcurve through f3 is very steep, showing that 4the lter discriminatessharply against frequencies just Byso designing the filter that f2 isabove f3, (Fig. 2) for the upper limit of the transmitted band. and byso proportionin the impedanees that f2 is below f8 (Fig. 3 the sameproperty may be secured for the lower limit. More- 2, the attenuationwhen' outside the transmitted band.v

the sharpcut-off may be attairnxdv over, where it is desired to'discriminate parv ticularly against some pre-determined fre-l quencyoutside the transmitted band, the filp ter may be so designed that ithas infinite stants but independent of eachother, chosen at will. Two ofthese may be takenl attenuation for this frequency provided there is noenergy dissipation in the filter.

I shall now give certain convenient mathematical formulae by means ofwhich any one skilled in the art may design a filter of the typedisclosedherein, tol meet the requirements in any' particular practicalcase.

The design of the filter involves the derivation of the values of thefour constants L1,

L2, C1 and C2. These values may, of course,

be chosen at will, and the properties of Vthe filter computed therefrom,but in the general case thereverse procedure will be 4 venient, i. c.,to choose the properties of the filter (according to the conditionsunder which it' is to 4be employed) and to calculate the values whichthe constants of the filter must have to give it these properties. tSince therearefour independent constants to be determined, it followsthat anyfour properties of the filterv dependent upon the conas thefrequencies fo and fsthus defining the range of free transmission',- thethird as f2,

the frequency of infinite attenuation, and

the fourth, as the impedance of the filter, this factor being ofimportance because it is desirable to make the saine substantially equalto that of 'the circuit into which the filter is placed, in order thatreflection losses may be avoided. The relations which exist 'between theabove-mentioned properties of the filter and the quantities L1, L2, C1,C2, will now be set out in mathematical form.

'In the Campbell patents hereinbefore mentioned, it was shown (equations3 and 4) that for a periodic structure of the type now underconsideration, in which the series impedance per section is Z1 and theshunt impedance persection is Z2, there is unattenuated transmission forall frequencies of currentfor which the value,of,-f

i/zla so that the limiting values fsandffo) of the +1 lies betweeni 1,.-(1) frequencies for free transmission may be determied from thefollowing equations:

. In the present case the values of Z1 and Z2 in terms of frequencyare'- zzfile-CQ (4) Where i is the imaginary operator 1/ 1 and p, theangular velocity, is written for 2wf, for. sake of convenience.

. equation (2) the resultant mentioned may be vention is not limited toany I of termination.

When', therefore, the values of Z1 and Z2, as given by (3) and (4), aresubstituted in vexpression may be solved for p, one of the roots, p2,deter- `mining one limiting frequency, f3, and the other, p0, the otherlimiting frequency, fo:

IIlhe relation which exists between the' valuessof -tlic constants ofthe filter and the frequency, f2, at which the attenuation is infinite,may be determined by placing the expression (eiation 2 of thevhereinbeforeampbell patent) for cosh Where is the propagation'constant,equal to infinity:

Thefrequencies fo, kf1 and f2 are thus expressed `in terms of theconstants of the lter. It remains to' evolve an expression for theimpedance of the filter.

This impedance varies With frequency, and it has been found convenientin the art to specify in design the' impedance at the frequency, termedmid-frequency, which is the geometric mean of the limiting frequenciesof the transmitted range, i. e.,

A filter is defined to have mid-'series termination when it isterminated by a series impedance of half that of the normal seriessection. This is illustrated in Fig. 4 in which the normal seriesimpedance is ZJ and the left terminal impedance is 1/2Z1,

1. e., composed of 1/2L1 and 2C1.` The filter may be assumed to have an4infinite number of sections toward the -ri-ghtso that the impedance atany other mid-series section, such as that which extends to .the rightfrom line l-I is the same as the impedance measured at the terminalsLf-b. Consequently, if Zms designates theniidseries section impedance,

substituting for and Z2, their values as given by equations (3) and (4),and simplifying, it will be found that the impedance at the frequency isgiven by the expression inid-series. v

Equations (5), (6), (7) and (10) are four simultaneous equations1nvolving the factors p2, p0, p3 and Zms, the values of which may beassumed, and the factors L1, L2, C1 and C2, the values of which are tobe determined. These equations may therefore be solved for the values ofthe last mentionedquantities,

I and when this is done itwillhe found that @Fm-P5' (12) @Femm (14)ZmsPZ2 l p0) The constants of the filter may' consequently l bedetermined by merely substituting the assumed values of p0, p2, p, andZms in the above equations.

For example, where, it is desired to construct a filter whose band offree transmission shall extend from 400 to- 2000 cycles, whose maximum(theoretically infinite) attenuation shall be at 2300 cycles and whoseimpedancezat mid-'frequency shall be 800 ohms,I (when terminated by amid-series section) so that the filter' may be inserted in a line of #14N. B. S. gauge open wire line (the characteristic impedance of which is,roughly, 800 ohms) we have, according to the notation used herein:

@Fac (4o0)=25ia )93:27: (2000) :12570. @Fae (2300) :14451. Zm=soaSubstituting thesevalues in equations (11) to (la), and solving gives:

L1: .0798 henries,

L2=.0594 henries,

(3l-:1.98 microfarads,

02:.0807 microfarads,` as the constants of the normal filter section.

'With tlie'mid-series termination assumed herein the values of the firstand last series inductance and capacity are, respectively, .0399 henriesand 3.96 microfarads.

Although I have herein shown and described only one form and arrangementof apparatus embodying my invention it is readily understood thatvarious changes and modifications may be made'therein with the scope ofthe following claims without de-x parting from the spirit and scope ofthe invention.

1What I claim is: l 1. A wave filter for an electric circuit,

said filter having a plurality of like recurrent sections,- each sectioncomprising lumped impedance in series with the circuit and lumpedimpedance adj acently in shunt thereto,fboth of said impedances beinglike types of resonant circuits' and so proportioned that the filterapproximately suppresses all frequencies lying 'outside apre-assignedband extending ibetween two frequencies 4other than zero orinfinity and substantially completely suppresses 'a certain pre-assignedfinite frequency other .than zero. 2. A recurrent' section .wave filterfor an electric circuit, each section consisting' of lumped impedance.in seriesv with the circuit and lumped impedance of like-type adja-`cently in shunt thereto, whereby said filter transmits freely allfrequencies lying within two finite limiting frequencies, butapproximately suppresses the frequencies outside of the said frequencyrange and dis criminates sharply against frequencies close to one ofsaid limits.

3. A wave lfilter for an electric circuit, said filter having aAplurality^of like recur.- rent sections, each section consisting ofv alumped inductance and capacity'-in series with each other inserted inseries with the circuit andI a 4lumped induc'tance and ca# 'pacity inseries with each other connected in shunt to the circuit, adjacently tosaid first-mentioned inductance and capacity.

4; A wave filter for an electric circuit,

consisting of a resonant circuit in series with the circuit and a liketype of resonant cir- 'cuit in shunt to the circuit, each of` whichdetermined by a finite frequency other than zero at which theattenuationof the "filter is approximately infinite, the impedance ofthe'filter, and the limiting frequencies of a pre-assigned band of freetransmission, which limiting frequencies are other than zero orinfinity.

5. A Wave filter for an electric circuit, said filter having a pluralityof like recurrent sections, each section consisting` of lumped impedancein series with the circuit and lumped impedance in shunt thereto, thesaid impedances being so proportioned that the attenuation of the filterhas a finite value at a chosen finite frequency and decreases, as thefrequency is changed in one direction, until it is substantially equalto zero at `a certain other finite frequency, remains at this valueuntil stillanother finite frequency is reached, then.A increases untilit becomes approximately infinite at still another finite frequency andthen decreases with further change of frequency in the same direction.

6. A Wave filterv for an electric circuit, said filter having aplurality of like recurrent sections, each section consisting of lumpedinductance land capacity in series Witheach other and in series in the'circuit and resonant at a certain frequency, and each section alsoconsisting of lumpedl inductance and capacity in series with each otherandI in shunt to the circuit and resonant to a certain other frequency.

7. A Wave filter for an electric circuit, said filter having a pluralityof like recurrent sections, each section consisting of lumped impedancein series with the circuit and lumped impedance of like type adjacentlyin shunt thereto, one such impedance being resonant at one frequency andthe other such impedance being resonant at another frequency.

8. An electr-1c Wave filter'consistlng of a connecting line ofnegligible attenuation containing lumped impedance in series with theline and lumped impedance pf like type in shunt 'across the line, saidimpedances having precomputed values dependent upon the upper limitingfrequency and the lower limiting frequency of a range of frequenciesitmis desired to transmit Without attenua-A ing frequencies.

Y9. Anelectric wave filter consisting of a approxiline composed of aplurality of sections, each section including a condenser and aninductance coil constituting an impedanceI in series with the line and acondenser and an inductance coil associated in like manner andconstituting an impedance in shunt across the line, said condensers andinductance coils having precomputed values dependent up`on the upperlimitingffrequency andthe lower limiting frequency of a range offrequencies it is desired to transmit Without attenuation, the lvaluesof said` condensers and said inductance coils being so proportioned thatthe structure transmits with practically negligible attenua-tionsinusoidal currents of all frequencies lying between two limitingfrequencies, While attenuating and approximately extinguishing currentsof y`neigh,boring frequencies lying Outside of said limitingfrequencies.l

In testimony whereof, I have signed my name to this specification this23rd day of April, 1920.

WILLIAM H. MARTIN,

